Use (positive) lookahead so that the regular expression asserts that the special character exists, but does not actually match it:
string.split(/
(?=?[a-zA-Z0-9]+;)/g);
See it in action:
var string = "aaaaaa
† bbbb
‡ cccc";
console.log(string.split(/
(?=?[a-zA-Z0-9]+;)/g));