Yes, you can get money for college from the military. If you serve more than 36 months on active duty, you could currently get 100% of in-state tuition and a monthly housing allowance paid for, for a maximum of 36 months. Note that the rates are subject to change.
http://www.benefits.va.gov/gibill/resources/benefits_resources/rate_tables.asp
Though think hard about joining the millitary if your only motivation is financial. 20% of non-institutionalized veterans are estimated to have a service-related disability, and a quarter of them have a disability rating of at least 70%. Examples of disabilities that qualify for a 70% rating: amputation of your dominant hand; a traumatic brain injury that results in inability to communicate in verbal or written language at least half of the time; burn scars on your face that result in gross disfigurement; or loss of one eye and a 20/200 rating on the other (that means that you could only read the top line of a standard vision chart).
Not something I’d personally want to risk, only to save money on college.
If you already have a work permit and are just waiting for the green card, I’d personally just postpone college for a year and work in the interim.