"I want to be able to use different styles in one paragraph."
A "Paragraph style", as implied by the name, applied to a paragraph.
A Header is a particular type of 'paragraph,'
The end of a paragraph is determined by a 'paragraph break', contained in the 'return' character entered at that point. The return also forces the text following it down one or more lines, depending on the 'space after paragraph' setting.
I don't know it it's possible to set a zero or negative value for the 'space after' the Heading style paragraph you use for chapter headings, but you could try setting a 0 or negative value for space after for that style.
A second possibility, also not tested, would be to apply the header style (as it is now), then select everything after the part you want in the TOC and set the character style of the selection to match the font and weight in the body paragraphs. While this might work to make the body of the text fit your desired appearance, I suspect it would not produce a satisfactory TOC result.
Regards,
Barry