I have UC Care and have had this option for several years. It is not cheap, esp for family coverage, but I have been very happy with the options available to us. (I still have my Brown and Toland based internist and Ob-Gyn, and see both UC and Sutter based specialists. I have a chronic condition which requires visits to a number of specialists every year, and my daughter has a condition that requires annual labs and imaging.)
I'm in exactly this situation. I believe the only other option is to switch to UC Care (the PPO plan), which is much more expensive.
We have a similar healthcare situation in our family: specialist at UCSF, but want to have access to primary care nearer home in the East Bay. UC Care works fine for this. Costs more, but if you have a serious, complicated medical condition as we do, it is worth it. Best of luck.
I work for a UC and use UC Care. It's a bit more expensive, but you have the flexibility to choose where you want to go. UC Care is administered through Anthem Blue Cross and since you go to UCSF a lot, the copays may be lower since they are "in network".