Printers generally do not print background colors, especially HTML background colors. For websites, CSS style sheets can be setup to look a certain way for printers, but this is not a capability that we are able to adapt for the inbox or for campaigns at this time.
To offer recipients another way to print the campaign, you may download and include a PDF of the campaign from down arrow for the campaign. That way, recipients would be able to print a PDF that does include the full colors, etc. as intended.