You can implement a function:
Controller:
$scope.calculateAge = function calculateAge(birthday) { // birthday is a date
    var ageDifMs = Date.now() - birthday.getTime();
    var ageDate = new Date(ageDifMs); // miliseconds from epoch
    return Math.abs(ageDate.getUTCFullYear() - 1970);
}
HTML
{{ calculateAge(friend.birthday) }}
Or a filter:
app.filter('ageFilter', function() {
     function calculateAge(birthday) { // birthday is a date
         var ageDifMs = Date.now() - birthday.getTime();
         var ageDate = new Date(ageDifMs); // miliseconds from epoch
         return Math.abs(ageDate.getUTCFullYear() - 1970);
     }
     return function(birthdate) { 
           return calculateAge(birthdate);
     }; 
});
HTML
{{ friend.birthday | ageFilter }}
Age algorithm taken from this SO answer.
[EDIT] If the age is less than 1 year, and you want to show months, you can modify the ageFilter to calculate the month difference:
app.filter('ageFilter', function() {
     function calculateAge(birthday) { // birthday is a date
         var ageDifMs = Date.now() - birthday.getTime();
         var ageDate = new Date(ageDifMs); // miliseconds from epoch
         return Math.abs(ageDate.getUTCFullYear() - 1970);
     }
     function monthDiff(d1, d2) {
       if (d1 < d2){
        var months = d2.getMonth() - d1.getMonth();
        return months <= 0 ? 0 : months;
       }
       return 0;
     }       
     return function(birthdate) { 
           var age = calculateAge(birthdate);
           if (age == 0)
             return monthDiff(birthdate, new Date()) + ' months';
           return age;
     }; 
});
Demo Plunker - Age Function
Demo Plunker - Age Filter
Demo Plunker - Age Filter with Months < 1 year