Pass array index into children entries with jq

If you think the title of this post is off, so do I. I'm happy to reformulate but it's hard to explain.

Given this:

[
  {
    "A": "a",
    "B": "b",
    "C": "c"
  },
  {
    "D": "d",
    "E": "e"
  }
]

I want this:

[
 { index: 0, key: "A", value: "a" },
 { index: 0, key: "B", value: "b" },
 { index: 0, key: "C", value: "c" },
 { index: 1, key: "D", value: "d" },
 { index: 1, key: "E", value: "e" }
]

Now whether it's a single array in the end or something else, it doesn't really matter. What I'm really looking for is to transform those elements in the input array into key-value pairs, and add the index of that element from the array. So the first object in the array is "index: 0", second is "index: 1", etc.

I can get the index from the array just fine:

jq 'to_entries | .[]' sample.json 

which gives me:

{
  "key": 0,
  "value": {
    "A": "a",
    "B": "b",
    "C": "c"
  }
}
{
  "key": 1,
  "value": {
    "D": "d",
    "E": "e"
  }
}

And I can get the key-value pairs just fine too:

jq 'to_entries | .[] | .value | to_entries' sample.json 

which gives me:

[
  {
    "key": "A",
    "value": "a"
  },
  {
    "key": "B",
    "value": "b"
  },
  {
    "key": "C",
    "value": "c"
  }
]
[
  {
    "key": "D",
    "value": "d"
  },
  {
    "key": "E",
    "value": "e"
  }
]

but I can't figure out how to combine the two.