Good question, i had to try out and see if i could create a HttpModule to do what you are describing.
I didnt have any luck trying to read from the responsestream, but using the ResponseFilter gave me a way to capture the content. 
The following code seems to work pretty good, and i figured maybe you could use the code as a base. But remember this is just something i threw together fast, it has not been tested in any way. So dont use it in any production environment without proper reviewing/testing and such. Feel free to comment on it though ;)
public class ResponseLoggerModule : IHttpModule
{
    private class ResponseCaptureStream : Stream
    {
        private readonly Stream _streamToCapture;
        private readonly Encoding _responseEncoding;
        private string _streamContent;
        public string StreamContent
        {
            get { return _streamContent; }
            private set
            {
                _streamContent = value;
            }
        }
        public ResponseCaptureStream(Stream streamToCapture, Encoding responseEncoding)
        {
            _responseEncoding = responseEncoding;
            _streamToCapture = streamToCapture;
        }
        public override bool CanRead
        {
            get { return _streamToCapture.CanRead; }
        }
        public override bool CanSeek
        {
            get { return _streamToCapture.CanSeek; }
        }
        public override bool CanWrite
        {
            get { return _streamToCapture.CanWrite; }
        }
        public override void Flush()
        {
            _streamToCapture.Flush();
        }
        public override long Length
        {
            get { return _streamToCapture.Length; }
        }
        public override long Position
        {
            get
            {
                return _streamToCapture.Position;
            }
            set
            {
                _streamToCapture.Position = value;
            }
        }
        public override int Read(byte[] buffer, int offset, int count)
        {
            return _streamToCapture.Read(buffer, offset, count);
        }
        public override long Seek(long offset, SeekOrigin origin)
        {
            return _streamToCapture.Seek(offset, origin);
        }
        public override void SetLength(long value)
        {
            _streamToCapture.SetLength(value);
        }
        public override void Write(byte[] buffer, int offset, int count)
        {
            _streamContent += _responseEncoding.GetString(buffer);
            _streamToCapture.Write(buffer, offset, count);
        }
        public override void Close()
        {
            _streamToCapture.Close();
            base.Close();
        }
    }
    #region IHttpModule Members
    private HttpApplication _context;
    public void Dispose()
    {
    }
    public void Init(HttpApplication context)
    {
        _context = context;
        context.PreRequestHandlerExecute += new EventHandler(context_PreRequestHandlerExecute);
        context.PreSendRequestContent += new EventHandler(context_PreSendRequestContent);
    }
    void context_PreRequestHandlerExecute(object sender, EventArgs e)
    {
        _context.Response.Filter = new ResponseCaptureStream(_context.Response.Filter, _context.Response.ContentEncoding);
    }
    void context_PreSendRequestContent(object sender, EventArgs e)
    {
        ResponseCaptureStream filter = _context.Response.Filter as ResponseCaptureStream;
        if (filter != null)
        {
            string responseText = filter.StreamContent;
            // Logging logic here
        }
    }
    #endregion
}