You didn't specify what RDBMS you are using. In SQL Server you can create a foreign key using more than one column. The key should point to columns that are in a unique or primary key and you do have the required primary keys in tables B and C.
The definitions of tables A, B and C can remain as they are in the question.
The definition of table D would look like this in SQL Server syntax. Here the foreign key constraints are created using separate ALTER TABLE statements. Different DBMS may use somewhat different syntax.
CREATE TABLE [dbo].[d](
[aid] [int] NULL,
[bid] [int] NULL,
[cid] [int] NULL
)
GO
ALTER TABLE [dbo].[d] WITH CHECK ADD CONSTRAINT [FK_d_b] FOREIGN KEY([aid], [bid])
REFERENCES [dbo].[b] ([aid], [bid])
GO
ALTER TABLE [dbo].[d] CHECK CONSTRAINT [FK_d_b]
GO
ALTER TABLE [dbo].[d] WITH CHECK ADD CONSTRAINT [FK_d_c] FOREIGN KEY([aid], [cid])
REFERENCES [dbo].[c] ([aid], [cid])
GO
ALTER TABLE [dbo].[d] CHECK CONSTRAINT [FK_d_c]
GO
It works as expected in my test:
INSERT INTO a values(1);
INSERT INTO a values(2);
INSERT INTO b values(1, 1);
INSERT INTO b values(2, 2);
INSERT INTO c values(1, 1);
INSERT INTO c values(2, 2);
(1 row affected)
(1 row affected)
(1 row affected)
(1 row affected)
(1 row affected)
(1 row affected)
Now let's try to insert into D:
INSERT INTO d values(1, 2, 2);
Msg 547, Level 16, State 0, Line 1
The INSERT statement conflicted with the FOREIGN KEY constraint "FK_d_b".
The conflict occurred in database "TestDB", table "dbo.b".
The statement has been terminated.
These inserts go through, as expected:
INSERT INTO d values(1, 1, 1);
INSERT INTO d values(2, 2, 2);
(1 row affected)
(1 row affected)
OR you can use this syntax:
CREATE TABLE d2 (
aid INTEGER,
bid INTEGER,
cid INTEGER,
FOREIGN KEY (aid,bid) REFERENCES b (aid,bid),
FOREIGN KEY (aid,cid) REFERENCES c (aid,cid)
);
In this case the foreign keys would get some autogenerated names, but they will work the same:
INSERT INTO d2 values(1, 2, 2);
Msg 547, Level 16, State 0, Line 1
The INSERT statement conflicted with the FOREIGN KEY constraint "FK__d2__351DDF8C".
The conflict occurred in database "TestDB", table "dbo.b".
The statement has been terminated.
INSERT INTO d2 values(1, 1, 2);
Msg 547, Level 16, State 0, Line 1
The INSERT statement conflicted with the FOREIGN KEY constraint "FK__d2__361203C5".
The conflict occurred in database "TestDB", table "dbo.c".
The statement has been terminated.
These inserts work, as expected:
INSERT INTO d2 values(1, 1, 1);
INSERT INTO d2 values(2, 2, 2);
(1 row affected)
(1 row affected)
OR, you can use this syntax to give the constraints some meaningful names:
CREATE TABLE d3 (
aid INTEGER,
bid INTEGER,
cid INTEGER,
CONSTRAINT FK_d3_b FOREIGN KEY (aid,bid) REFERENCES b (aid,bid),
CONSTRAINT FK_d3_c FOREIGN KEY (aid,cid) REFERENCES c (aid,cid)
);