Edit in JSFiddle

var now = new Date();
var today = new Date(now.getFullYear(), now.getMonth(), now.getDate());
var jsonDate = "/Date(" + today.getTime() + ")/";

function ViewModel() {
    var self = this;
    self.dateOfBirth = ko.observable(jsonDate);
    
    self.formattedDate = ko.computed({
        read: function() {
            var dob = new Date(parseInt(self.dateOfBirth().substr(6)));        
            return dob.getFullYear() + '-' + (dob.getMonth() + 1) + '-' + dob.getDate();
        },
        write: function(value) {
            var parts = value.split('-');
            self.dateOfBirth("/Date(" + new Date(parts[0], parts[1] - 1, parts[2]).getTime() + ")/");
        }
    })
}

ko.applyBindings(new ViewModel());

Epoch: <input type="text" data-bind="value: dateOfBirth" /><br/>
Formatted Date: <input type="text" data-bind="value: formattedDate" />