Hi,
Add the UpdateSourceTrigger to the binding.For UI elements the default UpdateSourceTrigger is LostFocus.You can set the UpdateSourceTrigger=PropertyChanged inside the binding as,
<checkbox name="baseMapChkBox" ischecked="{Binding IsBaseMapChecked,Mode=TwoWay,UpdateSourceTrigger=PropertyChanged}" horizontalalignment="Center" verticalalignment="Center">
One more point, "IsBaseMapChecked" is the property that you defined and triggered the "IsChecked" property inside the propertychange method,you have to trigger the "IsBaseMapChecked" property inside the PropertyChanged event I think.ie.;
PropertyChanged(this, new PropertyChangedEventArgs("IsChecked"));
become
PropertyChanged(this, new PropertyChangedEventArgs("IsBaseMapChecked"));
Regards,
Vineeth