The chances that you will be awarded sole legal and sole physical custody, and maybe even with only supervised visitation granted to your husband, are very good.
Under Washington state law, the chances of your obtaining primary custody of the children are very good under the circumstances that you describe. There is also an opportunity to direct your husband to drug/alcohol treatment as part of the dissolution process. Consult with an experienced family law attorney in the county in which you reside.
The chances are very good that he will only be allowed supervised visitation until he can prove he is clean and sober for an extended period of time. It is not safe for the children otherwise.
Custody and parenting time decisions are made "in the best interests of the children" based on several statutory factors, and if one of the parties has substance abuse issues, this can certainly affect the determination of these issues. A court can order a parent to undergo random drug or alcohol screenings to monitor "sobriety," and if a parent tests positive for illegal substances, the court can order that the parent exercise only supervised parenting time until a sufficient period of negative tests have been obtained. I recommend you speak with an attorney to discuss the process involved with moving forward, and to help determine your best course of action.
You obviously need to file for a divorce or legal separation and let a court determine how to allocate parental responsibilities if you and your husband cannot agree to a reasonable parenting plan. The court will decide that based on the best interests of the child and can impose reasonable conditions or limits on your husband's access to the children. It isn't possible to say what "your chances" of anything are, but the court will apply some common sense to the actual facts and circumstances and do what is necessary to protect the children if his drinking and drug use is a threat to them.
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