There are following types of modes available in UIDatePicker:
UIDatePickerModeTime,
UIDatePickerModeDate,
UIDatePickerModeDateAndTime,
UIDatePickerModeCountDownTimer
With the following you can show time:
datePicker.datePickerMode = UIDatePickerModeTime;
But both date and time can not be shown.
What you can do is either subclass UIPickerView
or in after selecting the Date, prompt user to select time using the above pickerMode.