If your branch office clients (computers) can access the Internet through the DSL modem, then it's not just a modem. It's a modem/router.
What device do you use at the branch office for bridging with head office? Also if it's a bridge, the two offices should be on the same subnet (or at least the bridge device at the branch office should be on the same subnet as the home office). Otherwise, it's not really a bridge, but a series of routers.
With that out of the way here is what I suggest:
1. Connect branch office clients to DIR-615.
2. Connect DIR-615 to a switch via WAN port.
3. Connect branch office bridge device to switch.
4. Connect DSL modem/router to switch.
Open the DIR-615 interface. Configure the WAN to use the DSL modem as gateway. Set a static IP for the DIR-615. The bridge device should also have a static IP on the same subnet as the DIR-615 and the DSL modem.
Go to Advanced > Routing and enable a route (checkbox). Write, name - branch office, address: 192.x.x.0 (the branch office IP), metric 1, interface WAN, netmask 255.255.255.0, gateway: ip of bridge device. Then save settings.
This static route will mean that all request from clients to the 192.x.x.0-255 space will get routed through the bridge device. Everything else goes through the default gateway (the DSL modem).
Problem is if your head office will need to access things on the branch office, you will need to deal with double port fowarding for the required protocols etc.
I'm no longer using the the factory firmware on my DIR-615, but DD-WRT custom firmware, so I'm not sure if you can select LAN instead of WAN as interface when setting up routes. I did it after an online emulator of the interface and it only allows WAN. If it also allows LAN, then a separate setup would also be possible.