You noticed already that his words are not matching his actions. If you fall back on your word (another relapse and I am done), you both are not matching your words with your actions. That doesn't sound like a healthy combination for a relationship.
Since the longest he had in sobriety was 3 months, why not take a break of 6 months while you both work on your recoveries. 6 months of not dating with limited communication will give you both time to focus on becoming better. That will benefit you both and your child.
Later, if recovery is working for both of you ~ you establish healthy boundaries and try spending quality time together.