If turning up heads in any combination is an infection, you're right. However, if turning up both heads or a given coin as heads constitutes the infection, then your odds are still only 1 in 2.
The more accurate way to view this would be (assuming sex with an infected person always results in transmission of the infection): How many persons are in my target group? (Not every person on earth is likely to have sex with you, so you can reduce the target population to a reasonable level). Out of that population, how many have the disease?
That will tell you your odds of contracting the disease. If you are homosexual, you increase your odds two ways: one, your target population is smaller. And two, the proportion of that population infected with the disease is much higher than the general population.