Hey Trine,
After taking a look at your site, it looks like we may need some clarification on what you (and foxandq, of course) are looking to specifically change. If you’re talking about the background of the input fields themselves, you can try adding
background-color: rgba(255,255,255,0.1)
to the CSS for .mc_input. The last value can be altered up to 1 and down to 0 to change how transparent the background should be and the first three numbers can be altered to change the color itself.
It’s possible for a WordPress theme to have styles for input areas overriding MailChimp’s .mc_input class, in which case the aforementioned background-color change would also have to be applied there.
If the desire for a transparent background is on some element, though, can you tell us what that is?
Thanks.