OP when I initially read this thread I thought you were trolling as I find it hard to believe that someone who is non-white is unable to see the diverse characters in the programmes on CBeebies even when not particularly watching e.g. Waffle The Wonder Dog, YolanDa's Band Jam, Let's Go For a Walk and The Baby Club At Home. (I initially read this thread when I was watching In The Night Garden, which is bloody annoying. )
If you have a child who is considered an ethnic minority in this country then unlike children who are part of the white majority as a parent you need to plan ahead and be proactive whether this is in the toys they play with, the books they read, the friends they make and the other people of all ages that they are around so they don't feel like they are the other. (You may have felt your parents didn't do that for you, but your parents took you to see relations and family friends regularly. )
Even then as a PP has pointed out it isn't all plain sailing and you will get random questions and comments from your children where they are questioning their identity.
Other people have given you toys and books with black and brown characters and figures but to be honest if you aren't proactive and plan ahead then you will find that when you want a specific toy or book for a present you are unable to get it. This means you will end up buying items months or years in advance you end up giving as birthday or Christmas presents.
In regards to superheroes Spiderman hasn't been white since 2011 - www.marvel.com/characters He is now mixed ethnicity - black and Latino. In the last couple of years there has been load of Spiderman merchandise around to buy. The vast majority has spider web logo or spiderman in his costume on it, and doesn't show Miles Morales.
I agree with Sugarintheplum and other PPs that you and your husband need to make the effort to get your son and any other children you have, around people that look more like them as much as possible.
Both sports clubs and churches are use to people, including children, coming from far away to participate in their activities as they know if they suit an individuals circumstances whether that is disability, ethnicity, religion, culture, ability or anything else then people can stay with them for decades.
In addition it isn't weird to arrange regular play dates while your children are in primary school, with people you meet through those activities. My own elder siblings did this when they and their spouses - some of whom aren't black - moved away from London ensure their children met other children more like them.
One big thing that is missing is that you have a boy. With the issues that boys and men who are black and mixed ethnicity I am related to and I know have had, it is really important that your husband is aware and at leasts understands the difference in how he and your son are treated in the same circumstances. There are certain things that boys defer to their fathers over due to them being the same sex regardless of racial issues. If you, and more importantly your husband, are not aware of these issues then you can't prepare you son on how to deal with them if he meets them. You won't get this information and insight unless you around other black and mixed ethnicity people, and most importantly talk to them.