You can both certainly check bags through; but I gather the intent of your question has to do with payment or lack thereof. Assuming your companion has no status, I would expect that s/he would not be able to check bags for free starting at IAH, since (a) you are not checking in together and (b) their IAH-DFW is as I understand on a different PNR than the one you share. Either way I would expect at a minimum a charge from IAH-DFW; possibly if you both collect bags at DFW (short check) - then meet landside, and check in together on your long-haul, at least you would get the baggage allowance for that.
As for protection, if both legs are on AA, yes, generally AA will protect both of you even though there are separate PNRs to and from DFW. That said, let's say you do not misconnect but they do - they may be protected on another flight, but likely you would have to keep your original flight since you showed up on time. But that's my best understanding; others may see this differently.