How might I force a floating DIV to match the height of another floating DIV?

Wrap them in a containing div with the background color applied to it, and have a clearing div after the 'columns'.

<div style="background-color: yellow;">
  <div style="float: left;width: 65%;">column a</div>
  <div style="float: right;width: 35%;">column b</div>
  <div style="clear: both;"></div>
</div>

Updated to address some comments and my own thoughts:

This method works because its essentially a simplification of your problem, in this somewhat 'oldskool' method I put two columns in followed by an empty clearing element, the job of the clearing element is to tell the parent (with the background) this is where floating behaviour ends, this allows the parent to essentially render 0 pixels of height at the position of the clear, which will be whatever the highest priorly floating element is.

The reason for this is to ensure the parent element is as tall as the tallest column, the background is then set on the parent to give the appearance that both columns have the same height.

It should be noted that this technique is 'oldskool' because the better choice is to trigger this height calculation behaviour with something like clearfix or by simply having overflow: hidden on the parent element.

Whilst this works in this limited scenario, if you wish for each column to look visually different, or have a gap between them, then setting a background on the parent element won't work, there is however a trick to get this effect.

The trick is to add bottom padding to all columns, to the max amount of size you expect that could be the difference between the shortest and tallest column, if you can't work this out then pick a large figure, you then need to add a negative bottom margin of the same number.

You'll need overflow hidden on the parent object, but the result will be that each column will request to render this additional height suggested by the margin, but not actually request layout of that size (because the negative margin counters the calculation).

This will render the parent at the size of the tallest column, whilst allowing all the columns to render at their height + the size of bottom padding used, if this height is larger than the parent then the rest will simply clip off.

<div style="overflow: hidden;">
  <div style="background: blue;float: left;width: 65%;padding-bottom: 500px;margin-bottom: -500px;">column a<br />column a</div>
  <div style="background: red;float: right;width: 35%;padding-bottom: 500px;margin-bottom: -500px;">column b</div>
</div>

You can see an example of this technique on the bowers and wilkins website (see the four horizontal spotlight images the bottom of the page).

Here is a jQuery plugin to set the heights of multiple divs to be the same. And below is the actual code of the plugin.

$.fn.equalHeights = function(px) {
$(this).each(function(){
var currentTallest = 0;
$(this).children().each(function(i){
    if ($(this).height() > currentTallest) { currentTallest = $(this).height(); }
        });
    if (!px || !Number.prototype.pxToEm) currentTallest = currentTallest.pxToEm(); //use ems unless px is specified
        // for ie6, set height since min-height isn't supported
    if ($.browser.msie && $.browser.version == 6.0) { $(this).children().css({'height': currentTallest}); }
        $(this).children().css({'min-height': currentTallest}); 
    });
    return this;
};

You should wrap them in a div with no float.

<div style="float:none;background:#FDD017;" class="clearfix">
    <div id="response" style="float:left; width:65%;">Response with two lines</div>
    <div id="note" style="float:left; width:35%;">single line note</div>
</div>

I also use the clearfix patch on here http://www.webtoolkit.info/css-clearfix.html

I can't understand why this issue gets pounded into the ground when in 30 seconds you can code a two-column table and solve the problem.

This div column height problem comes up all over a typical layout. Why resort to scripting when a plain old basic HTML tag will do it? Unless there are huge and numerous tables on a layout, I don't buy the argument that tables are significantly slower.

I recommend you wrap them both in an outer div with the desired background color.

This code will let you have a variable number of rows (with a variable number of DIVs on each row) and it will make all of the DIVs on each row match the height of its tallest neighbour:

If we assumed all the DIVs, that are floating, are inside a container with the id "divContainer", then you could use the following:

$(document).ready(function() {

var currentTallest = 0;
var currentRowStart = 0;
var rowDivs = new Array();

$('div#divContainer div').each(function(index) {

    if(currentRowStart != $(this).position().top) {

        // we just came to a new row.  Set all the heights on the completed row
        for(currentDiv = 0 ; currentDiv < rowDivs.length ; currentDiv++) rowDivs[currentDiv].height(currentTallest);

        // set the variables for the new row
        rowDivs.length = 0; // empty the array
        currentRowStart = $(this).position().top;
        currentTallest = $(this).height();
        rowDivs.push($(this));

    } else {

        // another div on the current row.  Add it to the list and check if it's taller
        rowDivs.push($(this));
        currentTallest = (currentTallest < $(this).height()) ? ($(this).height()) : (currentTallest);

    }
    // do the last row
    for(currentDiv = 0 ; currentDiv < rowDivs.length ; currentDiv++) rowDivs[currentDiv].height(currentTallest);

});
});