I don't have JMP 12, but with JMP 13, I was able to hack the output by removing the .darkBackground and .border styles.
If that works for you, maybe someone on the JMP community could offer a way to do this with JSL. However, it's not recommended to modify the output as it could have unexpected side effects.
Please also note that when you use Interactive HTML, your data are included in the output whereas it is not with plain HTML. In recent versions of JMP, you can output Interactive HTML without including the data, by publishing with 'Publish Data' disabled. When you do, interactivity is limited to opening and closing graphs in the report, because data are required to provide interaction within the graphs.