Thank you for the well written response.
My generator does have an internal bonded-neutral but does not have any GFCI protected outlets which would trip once I plug it into the transfer switch. I could unbond the neutral in the generator but I use it at construction sites which could be dangerous to me and my help. I guess I could buy a generator where the neutral isn't bonded to the ground and use it just for my house but I don't think it is necessary. For the amount of time I use it to power my house I think I'll take a chance with this setup..