Base Interface for ISession and IStatelessSession

Sometimes it is useful to be able to use some basic session functionalities without knowing if they are implemented by an ISession or an IStatelessSession. So, I propose creating a new interface, something like ICommonSession or IBaseSession, containing the declaration of the common functionality between ISession and IStatelessSession, which would implement this new interface.
The declaration would be something like:

public interface ICommonSession
{
IDbConnection Connection { get; }
bool IsConnected { get; }
bool IsOpen { get; }
ITransaction Transaction { get; }
ITransaction BeginTransaction();
ITransaction BeginTransaction(IsolationLevel isolationLevel);
IDbConnection Close();
ICriteria CreateCriteria<T>() where T : class;
ICriteria CreateCriteria<T>(string alias) where T : class;
ICriteria CreateCriteria(string entityName);
ICriteria CreateCriteria(System.Type entityType);
ICriteria CreateCriteria(string entityName, string alias);
ICriteria CreateCriteria(System.Type entityType, string alias);
IQuery CreateQuery(string queryString);
ISQLQuery CreateSQLQuery(string queryString);
void Delete(object entity);
T Get<T>(object id);
T Get<T>(object id, LockMode lockMode);
IQuery GetNamedQuery(string queryName);
IQueryOver<T, T> QueryOver<T>() where T : class;
IQueryOver<T, T> QueryOver<T>(Expression<Func<T>> alias) where T : class;
void Refresh(object entity);
void Refresh(object entity, LockMode lockMode);
void Update(object entity);
}