How can there be Happiness without suffering? I always thought that in order to be light, darkness must exist, in order for us to appreciate a beautiful sunshine, rainy days must exist, for a food to be good, bad food must exist and so on, if you have only good things you will not appreciate or feel happy about it. (this is the common mundane view)

This kind of thought clearly doesn't fit with the concept of Nibbana, where there is only Happiness and no suffering at all, so Happiness in Nibbana is not relative, it is something absolute.

Can someone explain what is wrong with the thought that sees happiness as something relative, that needs to be compared with other things? Is Happiness in Nibbana a different thing that has more to do with peace and stability?
Light vs darkness is a better analogy to wisdom vs ignorance than happiness vs suffering. What you describe as happiness and suffering are just experiences. They belong to the Sankhara group in the five aggregates of clinging. Nibbana exists independently of the five aggregates. All experiences, whether they are pleasurable, painful or neutral, fall under the first Noble truth. So they all have the inherent nature of Dukkha. Nibbana is non-experiential and devoid of Dukkha.