That's curious: don't both beams share the same earth?

.
I'd start by pulling the lamp unit out, and putting the voltmeter (set to D.C. volts) from the earth terminal on the bulb holder to the dip beam power terminal (i.e. both the power and return on the actual bulb holder), and then same for main beam (obviously switching the appropriate beam on when testing). This tests the actual voltage across the bulbs: it should be the same for both main and dip, and just below the battery's voltage.
Then do the same going from the lamp's earth terminal to a known good earth, like the battery negative, if your meter's lead will reach (keep the meter switched to the DC volts setting, and the headlamps on).
When checking the earths, you shouldn't really see more than .3v max, anything over a volt indicates poor earth. I would suspect, however, that if the main beams are O.K., it's more likely to be a problem with the power side of the dip beam circuit: be very strange though: you're sure the mains are definitely giving full power?
If it's definitely not earth, then try headlamp wires, dip beam fuses, dip switch and make sure the bulbs are fitted correctly in their holders.
DDK Member1243 07741 273865. Home of the RY Austin 7 Trophy's and Austin Single Seat Racers