Computing overall bitrate of a transmitter with a two chunks package
Don't use fancy calculations which merely muddle up the problem. The header is $K$ bits where $K = Lk_1$; the body is $M$ bits where $M = Nk_2$. You are using a $[n_1, k_1]$ code to transmit the header which you do by dividing the $K$ bits of the header into $L$ chunks of $k_1$ bits each, encoding them, and thus sending $L$ codewords of length $n_1$ bits each. Total number of channel bits $= Ln_1$. Similarly, you send a total of $Nn_2$ channel bits ($N$ codewords of length $n_2$ each) giving a grand total of $Ln_1+Nn_2$ channel bits to send the $Lk_1+Nk_2$ "data" bits in the header and body.  So, the overall rate of the scheme is
$$R = \frac{Lk_1+Nk_2}{Ln_1+Nn_2}.$$
But be aware that some people refuse to acknowledge the information in the header as data and insist that actually only $Nk_2$ data bits are being transmitted; everything else is overhead. For these folks, the rate would be just
$$R = \frac{Nk_2}{Ln_1+Nn_2}.$$