Important? No. I am a Dutchie living in America and although I grew up with Dutch values, I am more Americanized than anything. I value my heritage, but I find it nearly useless in social aspects as an American. I am always longing for my "home" when I know that I am better off here and if I was there, I would want to be here.
If / when I have kids, I want them to be understanding of other cultures in general, but I will raise them to integrate into whatever country we happen to be living in, probably here.
What is more important is how they treat others and that they learn to live well wherever they are. I want them to know about other cultures, but I do not want to raise them as aliens in the country they are born in. It is far more important that they are raised with good values and that they can communicate and socialize with their fellow citizens. I see too many people celebrating their own cultures in a way that sets them apart from the culture they are living in. I don't want my kids setting themselves apart from others in ways that don't matter. My nieces all have little or no interest in the country their fathers came from and they are great without it.
That being said, I love learning about other cultures and eating their food, but that's it. Culture is interesting and eye opening, but what really matters in the end is how we love others.
If I was married to another foreigner, I would expect that our kids would be partially raised with her cultural values, but would want them to learn to be Americans first.