Hey Way too stressed;
This is a gut-check in your marriage. None of us can know how much you love one another or how every moment between you has played out. Only you can make the decision if your love and trust of him is strong enough to work through this.
Your husband is not indulging a fantasy. Don't believe it for a second. Men curious about homosexuality do not build profiles, they go to every extreme to conceal information and discourage contact from gay or bisexual men. Accept that the man you are married to will always be sexually attracted to men. This is a need, not a want, not something he's doing to hurt you, not something he can shut off any more than you can suck-it-up and start being a lesbian. There is also no reason to expect that his Bisexuality will just go away over time. Many bisexuals change in their attraction back or forth. It is not predictable and not able to be influenced. Even though you only found out recently, the man you fell in love with was a bisexual, the man you took your vows with was a bisexual, and the man who has been your husband for 10 years was a bisexual. It is a part of the man you love completely and part of what makes him who he is.
Your husband has lied to you for 10 years. The nature of that lie doesn't much matter. The issue is he deceived you coming into the marriage. I'm guessing you didn't clear it with your husband before snooping through his browser history and that you didn't immediately sit down and talk with him about what you found so you're keeping some secrets as well. Every marriage has secrets kept for the sake of the marriage. I have no reason to expect that he kept his bisexuality a secret to destroy the marriage or hurt you. You'll have to decide if the circumstances of his betrayal are such that you cannot find trust for him in the marriage. There is no reason for you to believe that your husband has broken his vows or ever will.
Yes you need to sit down and talk with him about this as soon as you're prepared for the discussion. Level with him how you found out, ask him to explain why he never told you he is sexually attracted to men. Explain to him why his bisexuality is threatening to you. Tell him you both need to address his sexual preference and how it is going to work in the marriage. This is a complex issue, it doesn't have to be settled in one night, in fact it may be more productive to open the discussion and give him some time to come to terms with how this is going to impact the marriage before continuing the talk. If you do adjourn the discussion it must always be agreed upon when you will sit down and talk it out again.
You are not the only person in a marriage with a bisexual person. Thousands of other women are going through what you are right now and likely more men. It takes work and communication and compromise.