If you do return here - there are some posts here that seem to be saying that a step parent (e.g., your DH) income is not really relevant in terms of a custody case. Although, I am sure it is a concern to you and your family in "real" life, which is true for anyone.
What was not discussed here, is that your income and employment, as the child's parent, is relevant.
The consequence to you then, in terms of your original question, is that your DH employment may not be considered a factor in persuading the court in your favor.
In reference to your concerns about the father, if you think he is not responsible enough or has bad judgement with regards to your child, that could be relevant in terms of making a legal request to modify custody. That is not something you have pursued thus far, it seems. Certainly, the fact that he has drug paraphenalia lying around and has been in jail suggests questionable judgement, to say the least.
Questionable judgement does not necessarily mean that the child's father does not love him nor want to spend less time with him. From your previous posts, I think you would agree with that. It sounds like they have excercised their time with him quite consistently.