Does Office 365 Home Premium come with ad-free outlook.com e-mail?

I think the simple answer in NO.

If you purchase Office 365 Home (which comes with a basic Outlook subscription), you need to buy the additional subscription to OUTLOOK do that you receive the full service version without any ads.

I pay $AUD37.95 per annum for OUTLOOK and $AUD12 per month for Office 365 Home. I have no problems with either service.

Microsoft is a "For Profit" business. Expect to pay and you will not be disappointed!

You misunderstand my question.  

I purchased Office 2016 for my Mac and Office 365 to work online.  Everything in Office works except that OUTLOOK in the 365 mode keeps showing me adsense ads on the right hand side.  I completely reject Outlook.com showing me ads when I have a paid subscription.  Yahoo does not show me ads!  I paid for the year subscription and get NO ADS when using my web browser.   I want the same with Outlook. If I don't get it, then Microsoft does NOT get the rest of my employees as customers.  I don't get ads shoved down my throat with One Note online?  Why Outlook?  This madness has to stop, or Microsoft quickly becomes the last choice for business software in my organization.

No consumer Office version includes any mail account, it does in most cases include MS Outlook a mail client to which you add the mail provider of your choice

outlook.com is a completely separate service

Where did you get this information??