How I setup my NHibernate configuration to use Sqlite for unit tests.

ConfigureToUseSqlite

        public static void ConfigureToUseSqlite(this IKernel kernel)
        {
            var nHibernateConfiguration = Substitute.For<INHibernateConfiguration>(); // custom interface
            var msSqlConfiguration = SQLiteConfiguration.Standard
                .InMemory()
                .ShowSql()
                ;

            nHibernateConfiguration.GetPersistenceConfiguration().Returns(msSqlConfiguration);

            kernel.Rebind<INHibernateConfiguration>()
                .ToConstant(nHibernateConfiguration)
                .Named("MyNamedDatabaseConfiguration")
                ;

            var configuration = kernel.Get<global::NHibernate.Cfg.Configuration>("MyNamedDatabaseConfiguration");
            configuration.Properties["connection.provider"] = typeof(PersistentInMemorySqliteConnectionProvider).AssemblyQualifiedName;

            var session = kernel.Get<ISession>("MyNamedDatabaseConfiguration");

            var schemaExport = new SchemaExport(configuration);
            schemaExport.Execute(script: true, export: true, justDrop: false, connection: session.Connection, exportOutput: Console.Out);
        } 

PersistentInMemorySqliteConnectionProvider

    public class PersistentInMemorySqliteConnectionProvider : DriverConnectionProvider
    {
        private IDbConnection _persistentConnection;

        public override void CloseConnection(System.Data.IDbConnection conn)
        {
            // do nothing
        }

        public override System.Data.IDbConnection GetConnection()
        {
            EnsurePersistentConnection();
            return _persistentConnection;
        }

        private void EnsurePersistentConnection()
        {
            if (_persistentConnection == null)
            {
                var sqliteConnection = new SQLiteConnection("Data Source=:memory:;Version=3;New=True;");
                sqliteConnection.Open();
                _persistentConnection = sqliteConnection;
            }
        }

        protected override void Dispose(bool isDisposing)
        {
            base.Dispose(isDisposing);
            if (_persistentConnection != null)
            {
                _persistentConnection.Dispose();
                _persistentConnection = null;
            }
        }

    }