In Access and in VBA the 'date' data type is a floating point number that stores the date AND time in the same field/variable. Given the application you describe--where your times may span from one day to the next--I would store complete date/time information for every data point. Anything less and you can't reliably do math with your data, like to calculate elapsed times, which would be a waste.
What I might do in that case is provide a data entry form that is not bound to the table data, then error check the data entry, prompt the user to confirm that times after midnight do indeed occur on the following day, and then add the date data to the time data before saving it to the table. That would give you maximum control without expecting your user to enter dates AND times for every data point.
Keep in mind that date formats that you might apply have no impact on what is stored in the table. Date formats alter output, not input.