Authorities seek to seize more than $39 million in assets related to the case, including multiple bank accounts; a mansion in Raleigh, N.C.; $2.6 million in artwork; multiple Mercedes-Benz vehicles; and a Ruger pistol with an obliterated serial number, according to the indictment, which was unsealed Wednesday.

Mr. Teyf took part in the $150 million scheme between 2010 and 2012, when he was an executive at a Russian military contractor, prosecutors alleged. Others involved in the scheme received some of the money; Mr. Teyf, his wife and others transferred some funds into the U.S., including about $39.5 million into accounts held at Bank of America , prosecutors said.

Nearly all of the assets transferred to the Bank of America accounts were moved from places seen as red flags for money laundering, prosecutors said. One account received $14.7 million in wire transfers from accounts in Belize, the British Virgin Islands, Hong Kong, Panama and the Seychelles, prosecutors said. Of the accounts from which these funds originated, prosecutors said, more than $13 million came from Cyprus and the rest from Hong Kong.

The Teyfs were arrested last week, according to court records, on the same night that local media reported that authorities raided their home. A call to the family’s home wasn’t answered. A lawyer for Mr. Teyf didn’t respond to a request for comment.

They were charged along with Alexsy Timofeev, a Russian citizen living in Illinois who is alleged to have helped the couple with the money-laundering scheme while providing financial and auditing services for an Illinois trucking company for which Mr. Teyf was listed as president. Also charged was Mr. Timofeev’s wife, Olesya Timofeeva, with conspiring to harbor an undocumented immigrant. They were arrested Monday, according to court records. A fifth defendant, Alexei Polyakov, was charged with naturalization fraud.

Mr. Timofeev didn’t answer a phone call to a number listed for him. Mrs. Timofeeva and Mr. Polyakov didn’t respond to messages seeking comment. Lawyers for Mr. Timofeev, Mrs. Timofeeva and Mr. Polyakov couldn’t be identified.

During the course of the investigation into the money-laundering charges, a confidential FBI source learned that Mr. Teyf suspected his wife was having an affair with another man, prosecutors said. Mr. Teyf then recruited that source to help plan the man’s murder, either to take place in the U.S. or in Russia after they conspired to have him deported, prosecutors said.

Investigators said in court documents that John Patrick Cotter, a longtime friend and business partner of Mr. Teyf, aided Mr. Teyf in a plot to target the man. Mr. Cotter, who was arrested on allegations he bribed a public official, and a lawyer representing him didn’t respond to requests for comment. Mr. Cotter wasn’t named in the indictment charging Mr. Teyf and the others.

Mr. Cotter tried anonymously reporting to federal agents a marriage fraud involving the man Mr. Teyf suspected of having the affair, investigators said. Later, according to investigators, Mr. Cotter arranged meetings with Mr. Teyf and U.S. federal agents, acting as Mr. Teyf’s interpreter. These meetings were recorded, investigators say.

At one meeting, investigators said, Messrs. Teyf and Cotter agreed to pay $25,000 to a Department of Homeland Security agent in exchange for an investigation that would result in the arrest and deportation of the man they suspected of having the affair. Mr. Cotter suggested $10,000 down payment at the meeting, which Mr. Teyf provided after going back to his car to retrieve the funds, according to investigators. Mr. Cotter kept tabs on the deportation effort, investigators said, holding calls and arranging further meetings with the agent to discuss the matter.

When the deportation effort took longer than expected, Mr. Teyf returned to his original murder-for-hire plan, paying a confidential source $25,000 to kill the man before the end of 2018 and supplying the source with a firearm with the serial number removed to carry out the killing, prosecutors said.

Write to Samuel Rubenfeld at samuel.rubenfeld@wsj.com