On R-1 visa, the person may be employed and receive payments only from the religious organization which filed a petition for R-1 visa.
He/she may receive a compensation as an employee - reporting on the form W-2 - http://www.irs.gov/pub/irs-pdf/fw2.pdf
or as self-employed individual - reporting to 1099-misc - http://www.irs.gov/pub/irs-pdf/f1099msc.pdf
but only from the sponsored organization.
He/she may not have a side business or have another earned income - that would be a violation of the visa terms.
The same is true for the dependent on R-2 visa.
However - the person may have investment or passive (unearned) income - may have a rental income, royalty income, may receive dividends from investment, etc.