Try tomcat7 from backports in Jessie, no problem with it, Alfresco works fine.
ii libservlet3.0-java 7.0.75-1~bpo8+1 all Servlet 3.0 and JSP 2.2 Java API classes ii libtomcat7-java 7.0.75-1~bpo8+1 all Servlet and JSP engine -- core libraries ii tomcat7 7.0.75-1~bpo8+1 all Servlet and JSP engine ii tomcat7-common 7.0.75-1~bpo8+1 all Servlet and JSP engine -- common files