Hi, I'd like to help you with your question.
Your husband's issues with lying to you about money has made it very difficult for you to find a way to deal with the finances. Although you do not want to infringe on his independence with his money, he is showing you that he is not able to handle his own money or the household money.
This issue needs broken down into two parts. The first part is the money issues themselves. If your husband is lying about how much he makes and what he can afford to contribute to the household, then that leaves you to deal with the bills on your own or make up the difference that he is being dishonest about. Your choice is to either let this go on, which you have said is an issue for you, or to take action. Your husband is not addressing this issue and does not seem willing to (I'm assuming you have talked with him about it and he hasn't improved). So setting down some new rules is a good idea. Letting him know that you need to take over paying the bills and he has to give you X amount of dollars each month is very reasonable. It is not uncommon for one partner in a relationship to handle the bills and ask for a set amount. And you will set aside any extra for the next month so this is fair. If it helps, tell your husband that you will go over the bills with him each month so he is fully informed of what you are doing.
The second issue here is why your husband is lying to you. It sounds like he has an issue with being open and honest, which is not good for your marriage. Not only does it undermine the trust between you, which is vital for your relationship to grow, but it also creates hostility between you. It also gives you the message that your husband either does not trust you, or he is too immature to handle his own money.
Let your husband know that you would like to resolve this issue because it is hurting your marriage. Talk to him about seeing a counselor together to address this issue. To find a therapist, ask your doctor for a referral. Or search on line at http://therapists.psychologytoday.com/rms/.
If your husband refuses to go, go to therapy without him. You need the support to find a way to address this issue.
Also, learn more about why someone lies. It may help you pinpoint what is going on with your husband and find better ways to talk with him:
When Your Lover Is a Liar: Healing the Wounds of Deception and Betrayal by Susan Forward and Donna Frazier
The Truth About Lying: Why and How We All Do It and What to Do About It by Gini Graham Scott
You can find these books on Amazon.com or your local library may have them for you.
I hope this has helped you,