It's up to you to decide if IPersistent should be declared in Common or Service assembly. The best practice (usually) is to declare interfaces in a separate assembly for better layer separation. You need to take into account things like how often developers will create implementations of IPersistent, is it really need to be loose coupled, etc.
IPersistence is a concern for you DA and a means for your BO to communicate through it. That relationship should end there. Your UI should only know your BO and if you need to define a new interface to support "coding to contracts" define a new one in your BO. Your UI and BO should have separate concerns for what they do within the system.
For example, the IPersistence interface is going to define specific tasks for persisting the record to the database. You don't want that in your UI because it would be bypassing your BO. So unless you want an anemic BO, which really doesn't do anything and shouldn't be there at all, define something new at that level that relates to supporting your business logic.