How do you know that your Mailchimp emails are going to junk? Are you getting that assumption from the open rate?

One thing you should ensure is that you have added the Mailchimp SPF records and DKIM records for your domain.

Another thing to know, Mandrill is for transactional type emails: Order confirmations, etc. I would need to read the terms of use, but using it for blanket email campaigns probably isn't allowed.

For more information on avoiding spam filters with Mailchimp check out their guide here.

By the way, I run a couple email accounts and have around a 67% open rate for one, and 90% open rate for the other, so simply adding SPF records and DKIM records should help. Also, don't email people too much.