Ad-free Outlook.com does NOT come with your Home 365 subscription. You will still get ads as if you were a regular "free webmail" user.
Apparently Microsoft's view is that Outlook.com and your purchase and reliance on client side programs such as Outlook 2016, the use of which you are technically and exclusively purchasing by subscribing, are separate sub-MS-ecosystems. It would stand to
reason that once you subscribe to 365 and thus officially indoctrinate yourself as part of the MS line of working that ad-free Outlook.com would be included. It's not an unreasonable expectation. If you sign up with GSuites (formally Google Apps), for example,
this is exactly what happens. Ads across all services go away. For $5/month you have a business relationship (not a "free web user" relationship) that includes e-mail and a line of productivity applications. You feel like you're actually doing serious work.
That Microsoft would stutter, hesitate, or struggle with the same perspective is disturbing.