S.B.
M. - it is normal - in addition to your being her primary caregiver, she is also starting to identify with you because you are a girl. (beginning of gender identity) And also, she is starting the separation anxiety stage. So strike 3!!!
You didn't say how you were handling this, so I can't tell you if you're doing it right - not that there's even a right and wrong way...but you're concerned about the affect on your marriage, so obviously whatever you are doing, it doesn't matter if it's "right" as it's not helping with the harmony.
You didn't mention if you stay at home or work, but it does sound like you stay at home. So my advice is from that - I'd say you need to get her out and interact with other adults more so she gets a better comfort level with other people besides you. Separation anxiety at this age is really, really, tough as they are learning they are separate from you and that's pretty scary for them! So introduce new places and faces with you staying by her side to help to overcome the fears.
And as for at home with your husband, I'd suggest maybe your husband spend alone time with your daughter - where you actually leave the house - and let them work it out on their own. With you there to run intereference, she's more apt to retreat to her safety zone - you. So go sit at Starbucks for a half hour and read a magazine a few nights a week. She'll probably freak out when you leave, and maybe even the first time you're gone she may cry the whole time (because it's new). But your husband can come up with something "special" they can do together & then maybe she'll start looking forward to her daddy time.
And finally, yes, I promise it will get better! Okay, well, let me clarify - better with THIS particular crisis, and then she'll move right on to something else that will make you both crazy. Just stick with it, stick with each other, and try to laugh about things as often as you can.
Good luck - S.