The default definitions for this are in biblatex.def. In your case, they are:
\DeclareFieldFormat[article,inbook,incollection,inproceedings,patent,thesis,unpublished]{citetitle}{\mkbibquote{#1\isdot}}
\DeclareFieldFormat[article,inbook,incollection,inproceedings,patent,thesis,unpublished]{title}{\mkbibquote{#1\isdot}}
So you can add the following to your own .tex file (or to a biblatex.cfg):
\DeclareFieldFormat[inbook]{citetitle}{#1}
\DeclareFieldFormat[inbook]{title}{#1}
The first removes the quotation marks from your citations; the second from the bibliography.
\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@InBook{entry1,
author = {Author, A.},
booktitle = {Main Title of Book},
title = {InBook Title without Quotation Marks},
publisher = {The Publisher},
date = 3000,
location = {CityPlace},
pages = {63--90},
}
@article{entry2,
author = {Author, A.},
title = {Title of Article},
journal = {Journal Title},
volume = {50},
number = {3},
date = 3000,
pages = {63--90},
}
\end{filecontents}
\usepackage[style=authortitle,backend=bibtex]{biblatex}
\addbibresource{\jobname.bib}
\DeclareFieldFormat[inbook]{citetitle}{#1}
\DeclareFieldFormat[inbook]{title}{#1}
\begin{document}
\cite{entry1,entry2}
\printbibliography
\end{document}