There are tcpdump filters for HTTP GET & HTTP POST (or for both plus message body):
Run man tcpdump | less -Ip examples to see some examples
Here’s a tcpdump filter for HTTP GET (GET = 0x47, 0x45, 0x54, 0x20):
sudo tcpdump -s 0 -A 'tcp[((tcp[12:1] & 0xf0) >> 2):4] = 0x47455420'
Here’s a tcpdump filter for HTTP POST (POST = 0x50, 0x4f, 0x53, 0x54):
sudo tcpdump -s 0 -A 'tcp dst port 80 and (tcp[((tcp[12:1] & 0xf0) >> 2):4] = 0x504f5354)'
Monitor HTTP traffic including request and response headers and message body (source):
tcpdump -A -s 0 'tcp port 80 and (((ip[2:2] - ((ip[0]&0xf)<<2)) - ((tcp[12]&0xf0)>>2)) != 0)'
tcpdump -X -s 0 'tcp port 80 and (((ip[2:2] - ((ip[0]&0xf)<<2)) - ((tcp[12]&0xf0)>>2)) != 0)'
For more information on the bit-twiddling in the TCP header see: String-Matching Capture Filter Generator (link to Sake Blok's explanation).