I read the Cisco documentation of Cisco 3850 and have not found configuration to send email when interface is down. ASA can do this. I really appreciate if anyone know how to share the configuration.
You could utilize the Embedded Event Manager with a custom policy for this. There is a good overview and documentation here from Cisco: http://www.cisco.com/c/en/us/td/docs/ios-xml/ios/eem/configuration/xe-3se/3850/eem-xe-3se-3850-book/eem-policy-tcl.html
But this is relatively complicated. A much easier approach would be to forward the syslog output from the 3850 to your monitoring system and trigger the mail from there. Almost any monitoring systems have a syslog collector and can scan the messages for given keywords and trigger actions if such a keyword is detected.
Of course, this solution presupposes that you have some kind of system monitoring in place. But, whoever does not? ;)