It's important to realize that all molecular substances that can be liquid or solid have some forces that bond the molecules together. The hydogen bond is just one of them.
So when water mixes with an other liquid or dissolves a solid, some intermolecular bonds must be broken - some preexist in water, others in the other compound. Sometimes the new bonds are extremely favourable (ammonia, hydrogen chloride...) and the result is clear. Sometimes the change is neutral or slightly unfavourable, but it still happens to a variable amount because heat shuffles the molecules. Sometimes it's so unfavourable that nothing perceivable happens.
So "is there some hydrogen bond" doesn't suffice to answer "do they mix". Mixing water and alcohols of varied carbon backbone length needs to break some existing bonds. Do you see what bonds preexist and how the carbon backbone length influences this?
In a next step, you can imagine heterogeneous "mixes", or better colloids, where only one molecule end "mixes" with water, for instance soaps.