Can DLC transfer across console families?

Unfortunately, no. When you purchase DLC, you are buying the rights to play that song on that particular brand of console. There is no way to transfer or get credit for the DLC you have on one brand of console if you've decided to switch to another brand of console entirely -- for instance, you had a Wii and now you want a PlayStation 3, or you had an Xbox 360 and now you want a Wii. You'll need to repurchase any of the songs you wish to have on your new console.

Please note that this is not the same as transferring your purchased DLC to a newer or replacement version of the same console (for instance, if you buy a newer Xbox 360 or you get a new hard drive for your PlayStation 3). In most cases, it is possible to transfer DLC to a new/replacement console.