Any voltage can be measured with respect to any reference point you like, because the electric field has a value everywhere. Some reference points are more useful than others.
For example, if you put your one of your DC voltmeter probes in some arbitrary point in empty air, the electric charges making up the meter probe, and the impedance of the meter, disturb the measurement so much it looks like there is no effect. But if you held up your probes some distance apart while standing inside an oversized high-voltage capacitor, you'd get a reading — if you didn't cause it to arc over by being there.
(Another example, less relevant but to emphasize the point: there is some potential difference between two electric circuits that aren't wired together in any way. However, you can't readily measure it because as soon as you place a voltmeter between them, it discharges through the meter. We call these phenomena “electrostatic”, and in order to detect them you need special ultra-high-impedance electrostatic instruments — or for the difference to be large enough that you touch something and notice the shock of the sudden flow of current that equalizes the charge and potential.)
What reference point to use, in the specific cases you mentioned:
the voltages on the dipole
An ideal dipole is completely symmetric, so a good reference point, and probably the one that any analysis you've seen uses, is the center of the dipole.
the voltage … along the transmission line
Common transmission lines have two conductors; the voltage of interest is the voltage between those two conductors at some position along the line. (Other transmission lines are waveguides, which carry electromagnetic waves inside or outside a single conductor. In this case, there is still a potential difference but it is in the propagating electric field that is guided by the waveguide.)
If you want to relate the potential at a point on an antenna to a point on its feed line, then you have to take into account how the antenna is connected to the feed line — what matching devices are used at that interconnection — and also how the feed line is physically located (it is, after all, metal in the presence of an electromagnetic wave); there is no simple single answer.