Please link to the pattern whenever possible. It helps us help you.
If I'm understanding you correctly what you need to do is use the intarsia method of knitting. Intarsia is used for large blocks of knitting and is done flat. Fair Isle, or stranded, knitting is used for multiple colors across the work and is best done in the round.
There is a video at the video/advanced options tab at the top of the page. More information can be found here
The back will not be exactly the same as the front because you'll have the crossed stitches on it where you cross the colors to avoid holes. It's neater than Fair Isle though.