Wow, good looking contact page!
I would imagine you will have to code some hard CSS to get this going. I am not strong at it so I can only speak how I did it with my own background. You will have to do some homework as well.
You can include HTML in your form generating window.
<div class="something">
[text message id:msg]
[text name id:name]
[email senderemail id:email]
</div>
You can then define the “something” class to include the background. Using id such as msg, name and email you can define the height of the input, transparent background or fill it with a background. If you choose, you can edit the theme CSS but I find it easier to localize CSS in this case. You can include your CSS at the beginning of the form, such that:
<style>
.something {background:......}
input[type="text"] {background: transparent; border: none;}
#msg { }
#name { }
#email { }
</style>
<div class="something">
[text message id:msg]
[text name id:name]
[email senderemail id:email]
</div>
This is how I formatted my contact form, with background and custom input box height and background.
Also note that this may not work with all themes, so please test it out slowly, one style at a time. Good luck.