As it mentioned here: HttpClient Get images from response the DefaultHttpClient
/HttpClient
get's only one content, which is in your case it's an HTML page (served from: http://www.mysite/login.jsp). Than you need to parse that HTML page and get the specified img tag with it's src than you need only to download it (ONLY that, without resend the login.jsp request!). If you download a captcha image you need to get that image as soon as possible or it could be overwritten by another user, who tries to login.
As the browser does, you need to do the same way, download HTML, than parse it, than request all src/link/ect depends on what you need.
DefaultHttpClient
doesn't cache by default.
CachingHttpClient
cache is enabled by default, in this case you need to analyzes If-Modified-Since and If-None-Match headers in order to decide if request to the remote server is performed, or if its result is returned from cache. If there's no change on the server, you will get cached data, if you cached previously.