In truth, happiness is suffering in disguise but in such a subtle form that you don't see it. If you cling to happiness, it's the same as clinging to suffering, but you don't realise it. When you hold onto happiness, it's impossible to throw away the inherent suffering. They're inseparable like that. Thus the Buddha taught us to know suffering and see it as the inherent harm in happiness, to see them as equal. So be careful! When happiness arises, don't be overjoyed and don't get carried away. When suffering comes, don't despair, don't lose yourself in it. See that they have the same equal value.So according to Ajahn Chah's explanation, happiness is just a different form of suffering, no more and no less, and they are inseparable.
Which reminds me. I've also read in a motivational book years ago - I can't remember the title but obviously, the writer must have been a follower of Buddhism at heart - that in a similar vein, rain shouldn't be looked at as bad weather. There is only good weather, and the rain is just a different form of good weather. If we can accept that, then there is no problem.