How about using value.Address.City and value.Address.Street?? The most common way to access JSON data is through dot notation. This is simply the object name followed by a period and then followed by the name/property you would like to access. http://www.hunlock.com/blogs/Mastering_JSON_%28_JavaScript_Object_Notation_%29
For example,
$.each(data, function(key,value) {
    $('#companyDetails').append('<li>'+key+'<span class="ui-li-aside">'+ value.Address.Street + "," + value.Address.City +'</span></li>');
});
For detail coding,
<html>
<head>
    <script src="http://code.jquery.com/jquery.min.js" type="text/javascript"></script>
    <script type="text/javascript">
        function display(data) {
            $.each(data, function(key,value) {
                $('#companyDetails').append('<li>'+key+'<span class="ui-li-aside">'+ value.Address.Street + "," + value.Address.City +'</span></li>');
            });
        }
        $(document).ready(function() {
            var data = [
                {
                    "Name" : "ABC",
                    "Company" : "AA Company",
                    "Address" : {
                        "Street" : "123 Main Street",
                        "City" : "Yangon"
                    }
                },
                {
                    "Name" : "DEF",
                    "Company" : "BB Company",
                    "Address" : {
                        "Street" : "8941 Mandalay",
                        "City" : "NaypiDaw"
                    }
                }           
            ];
        display(data);
        });
    </script>
</head>
<body>
<div id="companyDetails"></div>
</body>
</html>
For you case that you do not know which data are in json file,
function display(data,flag) {
    $.each(data, function(key,value) {
    if ($.isPlainObject(value)) {
        if(flag == true)
        {
            $('#companyDetails').append('<b>' + "Company " + (key + 1) + '</b>');
        }
        display(value,false);
    }
    else
        $('#companyDetails').append('<li>' + key +  " : " +'<span class="ui-li-aside">'+ value +'</span></li>');
    });
}
In calling display function,
var flag = true;
display(data,flag);
Your output would be
I hope this would help.