I pronunciate with as wɪθ. (As far as I know it's wið in BrE). But for being practical, is it OK to pronunciate 'with the' as wiði or wiðə?
It's normally pronounced /wIθðə/, /wIθði/ (smallcap I)
The tongue position doesn't change (θ is not released), but the unvoiced /θ/ becomes the voiced /ð/ halfway through.
No, "with the" is not pronounced 'wither' or 'withee'. It's a definite double consonant, and if 'with' is
/wið/, it becomes /
wiððə/, with the ð given double value as in Italian double letters, for example.