Here are just the relevant code to adjust for the keyboard, and dismiss the keyboard when the user taps outside of the TextView (and keyboard).
I should note that the caveat is that my TableView is at the very bottom of the screen, so I don't have to figure out how it overlaps with the keyboard. If you have stuff below your TableView, you'll need to add some math.
public partial class myViewController : UIViewController
{
    UITapGestureRecognizer _tap;
    NSObject _shownotification;
    NSObject _hidenotification;
    public myViewController() : base("myViewController", null)
    {
        // This code dismisses the keyboard when the user touches anywhere
        // outside the keyboard.
        _tap = new UITapGestureRecognizer();
        _tap.AddTarget(() =>{
            View.EndEditing(true);
        });
        _tap.CancelsTouchesInView = false;
        View.AddGestureRecognizer(_tap);
    }
    public override void ViewWillAppear(bool animated)
    {
        base.ViewWillAppear(animated);
        // Register our callbacks
        _hidenotification = UIKeyboard.Notifications.ObserveDidHide(HideCallback);
        _shownotification = UIKeyboard.Notifications.ObserveWillShow(ShowCallback);
    }
    public override void ViewWillDisappear(bool animated)
    {
        // Unregister the callbacks
        if (_shownotification != null)
            _shownotification.Dispose();
        if (_hidenotification != null)
            _hidenotification.Dispose();
        base.ViewWillDisappear(animated);
    }
    void ShowCallback (object sender, MonoTouch.UIKit.UIKeyboardEventArgs args)
    {
        // This happens if the user focuses a textfield outside of the
        // tableview when the tableview is empty.
        UIView activeView = this.View.FindFirstResponder();
        if ((activeView == null) || (activeView == Customer))
            return;
        // Get the size of the keyboard
        RectangleF keyboardBounds = args.FrameEnd;
        // Create an inset and assign it to the tableview
        UIEdgeInsets contentInsets = new UIEdgeInsets(0.0f, 0.0f, keyboardBounds.Size.Height, 0.0f);
        myTableView.ContentInset = contentInsets;
        myTableView.ScrollIndicatorInsets = contentInsets;
        // Make sure the tapped location is visible.
        myTableView.ScrollRectToVisible(activeView.Frame, true);
    }
    void HideCallback (object sender, MonoTouch.UIKit.UIKeyboardEventArgs args)
    {
        // If the tableView's ContentInset is "zero", we don't need to
        // readjust the size
        if (myTableView.ContentInset.Top == UIEdgeInsets.Zero.Top)
            return;
        // Remove the inset when the keyboard is hidden so that the
        // TableView will use the whole screen again.
        UIView.BeginAnimations (""); {
            UIView.SetAnimationCurve (args.AnimationCurve);
            UIView.SetAnimationDuration (args.AnimationDuration);
            var viewFrame = View.Frame;
            var endRelative = View.ConvertRectFromView (args.FrameEnd, null);
            viewFrame.Height = endRelative.Y;
            View.Frame = viewFrame;
            myTableView.ContentInset = UIEdgeInsets.Zero;
            myTableView.ScrollIndicatorInsets = UIEdgeInsets.Zero;
        } UIView.CommitAnimations ();
    }
}
Thank you mickm for posting the Objective-C solution.