I believe that some, but not all wifi chipsets will allow 2 subinterfaces, one of them in master mode and one of them in client mode.
The difficulty is that there is only one radio. The client subinterface needs to search for the SSID it wants to join and set the radio to the same channel as the access point it associates to. Master subinterfaces, on the other hand, are normally set to a fixed channel. You may have difficulty getting things configured so that the two subinterfaces don't step on each other's channel settings. The usual tools for configuring wifi interfaces probably won't help you with that task. Hardcoding the channel number all around seems the best option.
One way or the other, you'll be stuck with both subinterfaces on the same channel, which means you only have half the bandwidth available, because the same traffic has to go in and back out on the same radio frequencies.