I asked much the same questions (save it was about 2-4-1's rather than MFU's) in November:

Optimum way to get to Costa Rica

Short answer, if 2-4-1'ing, it's separate tickets to MIA/DFW on BA and then on with AA.

Note, if you are looking at the summer, the BA flight to DFW arrives too late to connect with the AA flight to SJO.

As it's two tickets, others advocated IAH and then onwards with Continental.