No, they are not inverses.
If you put those filters in parallel their sum will match the original signal exactly.
Notch filters are not mathematically equal to the inverse of band pass filters.
I've tried to upload images of the different transfer functions, but something keeps messing up.
Here's a handout from a class that should show the difference. See pp. 6-8. http://users.ece.gatech.edu/mleach/ece4435/sp07/dp03sp07.pdf
Eq. 11 and 17 show the differences.
Would a "band reject" filter be a possible addition?
I imagine you can sum (ie., not placed in series) the outputs of a low pass filter and a high pass filter into a mixer?? If the lowpass cutoff freq is lower than the high pass cutoff freq, it will reject a band that is the difference between the two cutoff freqs. Strictly speaking I believe notches deal with one center frequency where band reject deals with a range, splitting hairs perhaps.
|reject|
____ ____
\ /
\ /
^ LPf ^ HPf