Whether you CAN do this depends on your bylaws, but, basically it's not a good idea. A "best practice" would be to keep these offices separate to preserve some of the checks and balances.
At one time, we had a married couple as President/Treasurer. Due to problems, we needed to take a hard look at these issues and tighten controls when we created our new bylaws. Consquently, ours state that two members of the same household can't both serve as officers. (Nor could the one person hold two offices.) The principle is somewhat the same, so bear with me.
However, we didn't want to back ourselves totally into a corner, so we added a proviso that the Board could overrule this with certain vote (2/3?).
If we were in a situation where we just didn't have any choice, we would add controls. In your case, you'd want a second signature on all checks. (Good idea, anyway) and you'd want a different officer to review the accounts and keep an eye the month to month financials (beyond the yearly audit). You want not only to minimize the risk of mismanagement of funds, you want to avoid the PERCEPTION that this could easily happen.
Find another way if at all possible. If not, then just be very open about it. "We don't want to do this, but there's no other choice. These are the extra precautions we'll take, and this plan has been approved by the Board."
And keep in mind, controls like this should not be considered an insult to the officer. They should be a routine part of doing business. Additionally, they can serve as protection for that officer's reputation (if they followed).
JHB explained it best with the checks and balances but I am a survior of having to wear several hats this past year as President and acting Secretary and between the VP and me keeping the books! When the Treasurer walks, the Secretary never shows and average attendance at a meeting is 5-10 parents INCLUDING the board, you do what you can! YOU BET I was held accountable for every sticking dime but these were the same people that would wlak away every night wanting nothing to do with being on the board! YOU BET that wall and hard place I was not fun, but would I do it again......ask me in a few years when my memory is a bit more forgiving..lol!