It's rather easy to set the Time Capsule in Bridge Mode and allow the AEBS to handle DHCP. You'll be able to use the Time Capsule as a secondary access point, creating another SSID for your network. Or you can even turn the wireless radio off entirely and have it connected as a device on your network.
In AirPort Utility, set Connection Sharing to Off (bridge mode) on your Time Capsule. Then configure the Wireless settings however you like. Afterwards, connect the TC's WAN port to one of the AEBS' LAN ports. In addition, you'll be able to use the TC's LAN ports to connect any wired devices (effectively gaining two LAN ports since you'll lose one on your AEBS to connect the TC).
Doing this will allow any computers connected to any SSID broadcast from either the AEBS or the TC to communicate with one another and to access the TC's HDD for backups.
This is how I had my TC set up before it bit the dust