As investigators puzzle over their motives, the couple — the husband born in Illinois and raised in Southern California, the wife born in Pakistan and recently living in Saudi Arabia — have emerged as one of the most perplexing pairs in the recent history of mass homicide. Their lives, and motives, remain mysteries to investigators, who are looking at possible ties to international terrorism but have not ruled out the possibility that this was the bloody culmination of a workplace dispute.

Mr. Farook and Ms. Malik were observant Muslims, described by friends as quiet and unobtrusive. Mr. Farook, 28, who was a lanky six feet tall and had a full beard for long periods of his life, graduated from California State University, San Bernardino, with a degree in environmental engineering. He worked for the San Bernardino County health department, checking food surfaces at restaurants and bakeries and chlorine levels in public swimming pools.

Image Syed Rizwan Farook, one of the suspects in the San Bernardino, Calif., shooting. Credit... California Department of Motor Vehicles

Far less is publicly known about Ms. Malik, 29, who lived with Mr. Farook and his mother in Redlands, about five miles from where the attack took place. Mr. Farook brought her to the United States in July 2014, with a Pakistani passport and a K-1 visa, which designated her his fiancée. He applied for a permanent resident green card for her in September 2014, and she was granted a conditional card last July after passing a background check.

In registering for one of two dating services he used, Mr. Farook said he spoke Urdu, though friends said the couple spoke to each other in English. Mr. Farook, in a posting on one of the dating services, said he was open to dating a woman of any faith but was looking for “someone who takes her religion very seriously and is always trying to improve her religion.”