@AngelWings606, I would agree that it would be very difficult (if not impossible) to simultaneously pursue a BArch and a degree in Bioengineering. This really begs the question of WHY you want to do this.
If you’re sure you want to be an architect and like the design/creative aspects of archiatecture, then the USC BArch is an excellent choice. If you’re not sure, then the UCB BA in Architecture would give you more academic flexibility. UCB’s MArch is highly regarded, though admission is competitive.
Another option would be to study bioengineering as an undergrad then if you’re still interested in architecture, get an MArch. MArch programs admit students from a wide variety of undergraduate backgrounds. You can major in architecture, engineering or just about anything else and get admitted to a top MArch program (as long as you fulfil the program’s entrance requirements.)
You should also bear in mind that the MArch is an expensive degree. Grants are available, but not guaranteed, so before committing to a career path, look at the total cost.