In reply to Kristof.

I would definitely recommend the entire website be moved to HTTPS with proper redirects set up for pushing all HTTP traffic over to HTTPS.

Google is moving more and more towards HTTPS and as of this month started sending our warnings to webmasters for what they considered violations for non-compliance.

Be ahead of the game and move to HTTPS now!

PS: Search Engine Land, Yoast, and Moz should all have good articles on maintaining SEO with HTTPS moves.