Thank you very much for the replies. We are still up in the air, but are leaning toward BC on the return flight, but we have nothing to really base that on.
To answer a few of ArizonaRoadWarrior's questions:
When cashing in our miles, we would prefer to be on BA (or, as a backup, IB, since it is the other airline that will get us to our destination with only one stop) over AA on the trans-Atlantic flights, but we will take AA if that is our only option – for basically the same reasons you laid out, we had have great experiences in BC and FC with BA, IB and JL. BC and FC in AA has been good to us, but the international airlines service seems to be consistently better. If we take AA to LHR, we will be on a 777. AA to MAD would be a 767-300. BA to LHR would be a 747 and IB would be an A340.
We called AA before posting this question to make sure we could, in fact, do this. We were told that it is possible to book 3 coach on one leg and 2 business on the other (unfortunately, yes, we will have to pay the 10% lap fee, plus taxes, although the agent told us it would be 10% of the lowest fare – I hope she’s right!)