Any character style will apply any specific font formatting in the style and then any font formatting in the underlying paragraph style.
Any font formatting, other than that in the underlying paragraph style, applied to the text prior to adding the character style will be removed. For purposes of this, direct formatting includes any other character style; you can only have one character style at time applying to text.
That is how it is.
You can create character styles that that combine various things. For instance, I have a style
Strong Emphasis that is both
Bold and
Italics.
You can have paragraph styles that have any formatting you want and that formatting will not change upon application of a character style unless changed in the character style.
Understanding Styles in Microsoft Word
Character Style v Paragraph Style v Linked Style