Within Firefox use LiveHttp headers pluggin to view the Http Headers responses from server. You will see the Status Code like HTTP/1.1 404 FILE NOT FOUND in there.
It will look like this:
I don't think there is a pluggin for IE but you could use Fiddler to analyse the web Traffic - it will show you in details all packets including Headers.
Here is how Fiddler looks:
To summarize: Browsers are created to interpret the Hyper Text not display all the content of the packets - this is the job for sniffers/debuggers. You can use mentioned above tools in Windows or tcpdump on Linux. As a side note - you could see Headers in Wireshark on Windows as well but this is overkill since you will see more then the network layer you need. You need only Application Layer and you would see That plus Network and Data Link layer in there as well.