EmployeeController.cs

using Dapper;

public class EmployeeController : Controller
{
    private IDbContext DbContext { get; set; }

    public EmployeeController(IDbContext dbContext)
    {
        DbContext = dbContext;
    }

    [HttpGet]
    public ActionResult Index()
    {
        var employees = DbContext.GetConnection().Query("SELECT * FROM Employees");

        return View(employees);
    }
}

NinjectMVC3.cs

private static void RegisterServices(IKernel kernel)
{
    var connectionString = 
        ConfigurationManager.ConnectionStrings["Database"].ConnectionString;

    kernel.Bind<IDbContext>().To<SqlContext>()
        .InRequestScope()
        .WithConstructorArgument("connectionString", connectionString);
}

SqlContext.cs

public interface IDbContext
{
    IDbConnection GetConnection();
}

public class SqlContext : IDbContext, IDisposable
{
    private readonly string ConnectionString;
    private static readonly object @lock = new object();
    private SqlConnection Connection;

    public SqlContext(string connectionString)
    {
        ConnectionString = connectionString;
    }

    public IDbConnection GetConnection()
    {
        if (Connection == null)
        {
            lock (@lock)
            {
                if (Connection == null)
                {
                    Connection = new SqlConnection(ConnectionString);
                    Connection.Disposed += new EventHandler(Connection_Disposed);
                    Connection.Open();
                }
            }
        }

        return Connection;
    }

    void Connection_Disposed(object sender, EventArgs e)
    {
        Connection = null;
    }

    public void Dispose()
    {
        if (Connection != null)
        {
            lock (@lock)
            {
                if (Connection != null)
                {
                    Connection.Dispose();
                }
            }
        }
    }
}