It's up to you & I'm not sure there is one right way to approach this. Is your wife comfortable going for marriage counseling? If she is, then probably it would be fine to start marriage counseling & individual counseling at the same time. Often marriage counselors will be willing to also meet with individuals separately outside of their shared session.
If your wife is not seeing the need for marriage counseling, maybe the best place to start would be individual counseling. It sounds like you are both happy in your marriage & just being overly concerned about the other person's happiness. If she's saying she's happy, I think you need to try to take her at her word. If she's making you happy, then tell her that & ask her to take you at your word as well. I think (though a professional could better direct you) that it could be the case that both of you are happy in your marriage, but unhappy to do other factors in each of your lives. If that is the case, then maybe you each could benefit from individual counseling. But, counseling is a personal decision & not everyone is comfortable going. And, even those who are comfortable with one type of counseling, may not be comfortable with another type of counseling. So it needs to be her decision whether or not she wants to go, but certainly you can make the decision to get help for yourself & maybe the progress you make would be an inspiration to your wife to get help for herself.
Keep us posted on what happens & let us know if there is anything any of the members can do to support you (realize that we have fewer people who post on weekends, so it may be Monday before you get many responses, but I imagine several people will be able to share their own experiences after the weekend as there have been many of our members who have gone through similar struggles).
Moderator -- Depression Forum