IEのみバージョン5以降

window.onbeforeprint = function() {
    console.log(This will be called before the user prints.);
};
window.onafterprint = function() {
    console.log(This will be called after the user prints);
};

Firefox (jquery読み込み)

(function() {
    var beforePrint = function() {
    console.log(Functionality to run before printing.);
    };
    var afterPrint = function() {
    console.log(Functionality to run after printing);
    };

    if (window.matchMedia) {
    var mediaQueryList = window.matchMedia(print);
    mediaQueryList.addListener(function(mql) {
        if (mql.matches) {
        beforePrint();
        } else {
        afterPrint();
        }
    });
    }

    window.onbeforeprint = beforePrint;
    window.onafterprint = afterPrint;
}());

Chrome

Firefoxと同じコードでafterPrintのほうが実行される