The 1990 Decennial Census contains very detailed "ethnic" data in several volumes. The most important are the following:
Social and Economic Characteristics CP-2: New Jersey, available in three parts [Part 1, Part 2, Part 3]
Contains tables on
The Foreign-Born Population in the United States CP-3-1
Contains much useful information, but the data is provided only at the national level
Ancestry of the Population in the United States CP-3-2
Contains much useful information, but the data is provided only at the national level
Persons of Hispanic Origin in the United States CP-3-3
Contains much useful information, but the data is provided only at the national level
Detailed Ancestry Groups for States CP-S-1-2
Contains much useful information, but the data is provided only at the state level