Hello Travis. For a variety of reasons related to performance and reliability, it's not recommended that you include an ArcGIS map service within another map service (aka "cascading" services). ArcGIS Server 10.1 won't even let you publish a service like this.
Instead, your client application should connect directly to the services. So you might have a layer in your web map that refers to your imagery basemap web service and a separate layer that refers to your business data such as snowplows, ATMs, homes for sale, or whatever it is you're mapping.
If you play around with the ArcGIS.com map viewer, you'll see how this works. The viewer loads a basemap service for you. And then you connect to other services and place them on top. You're able to make a nice mashup without embedding any service within another service.
Sterling