If you collect oxygen and hydrogen in a single tube, the volume reflects both. If you know that the molar ratio is 1:2, you can calculate the volume of hydrogen gas by multiplying the total volume by 2/3. If you want to verify the molar ratio without expensive instrumentation, you might consider a chemical reaction that only reacts with oxygen or only reacts with hydrogen.
There is a standard lab to determine the oxygen content of air. It uses steel wool to react with the oxygen (but not the nitrogen) in air, turning it into "rust". The volume change observed corresponds to the oxygen that reacts. A mixture of oxygen and hydrogen is explosive (more so at a ratio of 1:2), so I would keep it at a small scale and avoid sparks.
I'm sure there are also convenient reaction to use up the hydrogen while leaving the oxygen, but the most common search result on the internet is the reaction with oxygen, which would remove both oxygen and hydrogen from the gas phase rather than isolating one of them.