Klum, 38, filed her petition Friday, asking for primary physical custody of their four children, with Seal getting visitation rights.
Klum claimed there was a postnuptial agreement, meaning the couple shares no community assets. However, Seal's documents filed Tuesday claim there are "community and quasi-community" assets, which could put Klum's reported $70 million worth on the table. Both are asking the judge not to grant spousal support.
The couple jointly announced earlier this year that they were separating after seven years of marriage. Days later, Seal, 49, said on Piers Morgan Tonight that there was still a chance the couple would get back together.
Klum and Seal began dating in 2003 and got engaged in December 2004. They married in Mexico in May 2005. The pair has three children together: Henry, 6, Johan, 5, and Lou, 2. Seal adopted Klum's 7-year-old daughter Leni from Klum's previous relationship to Flavio Briatore.