MS does have military discounts for veterans
Stephan provided a link to a 10% discount page.
As well, check at the PX / Base Exchange that you qualify to shop at. They may have the licenses.
NOTE: if you do get a military discount for a 1yr 365 subscription remember that you have to go back to the PBX to get the explicit Military product key. If you let it auto renew it is most likely to renew using the 365 Home price.
Note: you can buy and activate up to 5 product keys for a 5 year term.
The "HUP" is a better deal, if you qualify (and it is still offered)
https://cloudblogs.microsoft.com/industry-blog/industry/government/military-discount-through-the-home-use-program/
https://enterprise.microsoft.com/en-us/articles/industries/government/federal/military-discount-through-the-home-use-program/
Here is an even older article. I have no idea if the code is still valid
<Snip
http://www.neowin.net/news/office-2013-now-available-through-microsofts-home-use-program-for-995
>
if you’re in the United States Army it’s as easy as entering your official Army email address (@mail.mil, @us.army.mil, etc.) and then using the code C4FAA257E3. It’s well worth checking out especially at the extremely low price.
</snip>
MAE is only available from Military Post exchanges, is an annual subscription only available to qualifying military members and retirees.
This current article identifies that military 365 licenses are going to be treated like 365 Home
2018 08 31- Significant improvements in Office 365 Consumer Starting Monday Oct 1 2018
https://office-watch.com/2018/significant-improvements-office-365-home-personal/
license allows you to share with up to 6 "family" members
each share is allowed up to 5 computers active at the same time
