I'm currently an upper level MSTP student (in the graduate phase) at Baylor. To answer your question, we have students that are working in labs at Baylor, Rice, Texas Children's Hospital, and MD Anderson. The main things that seems to govern where the student is the affiliation of the faculty member. Our thesis committees often have UT-Houston faculty (as our outside member) and many journal clubs are jointly run with UT-Houston. I see UT-H students at our seminars and I have been to plenty of seminars at MD Anderson. To me, although UT-Houston and Baylor are separate schools, the research faculty at both institutions are readily accessible.
In terms of the medical school, St. Luke's is jointly staffed by both Baylor and UT-Houston residents/students/faculty. They also share responsibility over Thomas Street, an HIV outpatient care clinic.