If what you need is to compare only time, ignoring date, then you should do something like this, so your 'date' part be equal in all three variables.
Boolean InBetweenTime(Date currentTime, Date startTime, Date endTime){
Boolean result = false;
//calendar for currentTime
Calendar currentCal = Calendar.getInstance();
currentCal.setTime(currentTime);
//calendar for startTime
Calendar startCal = Calendar.getInstance();
startCal.setTime(startTime);
//calendar for endTime
Calendar endCal = Calendar.getInstance();
endCal.setTime(endTime);
//set corresponding date fields of startTime and endTime to be equal t ocurrentTime, so you compare only time fields
startCal.set(currentCal.get(Calendar.YEAR), currentCal.get(Calendar.MONTH), currentCal.get(Calendar.DAY_OF_MONTH));
endCal.set(currentCal.get(Calendar.YEAR), currentCal.get(Calendar.MONTH), currentCal.get(Calendar.DAY_OF_MONTH));
//return true if between, false otherwise
return (!currentTime.before(startCal.getTime())) && (!currentTime.after(endCal.getTime()));
}