Well what is part of the blog and what belongs to the rest of the site will probably differ so it is hard to split. E.g. is header and footer the same? Anything else that is shared?
Anyway, here are two options:
1.Separate instances
If the blog and the rest of the site look totally different you may consider separate WordPress installs or a Multisite instance. This way you can have different themes for each of them.
2.Switch theme for blog URLs
You could just have a different theme and switch depending on where you are. This answer handles that. It switches on user agent which you’d need to adapt, but the theme switching part is explained pretty nicely:
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