Should you use a partial class across projects?

I have a class library with all my database logic. My DAL/BLL.

I have a few web projects which will use the same database and classes, so I thought it was a good idea to abstract the data layer into its own project.

However, when it comes to adding functionality to classes for certain projects I want to add methods to certain classes.

For example, my data layer has Product and SomeItem objects:

// Data Access Layer project

namespace DAL {
  public class Product { 
     //implementation here 
  }

  public class SomeItem {
     //implementation here 
  }
}

In one project I want to add an interface that is used by different content items, so I have a class called:

// This is in Web Project
namespace DAL {
  public partial class Product : ICustomBehaviour {

    #region ICustomBehaviour Implementation
       TheSharedMethod();
    #endregion
  }
}

Is it a good idea to write a partial class in a separate project (creating a dependency) using the same namespace? If it's a bad idea, how can I get this type of functionality to work?

It doesn't seem to want to merge them at compile time, so I'm not sure what I'm doing wrong.