Legally separated, spouse may file bankruptcy. What effect may this have on our jointly-owned home?

It depends what chapter she chooses to file. In California, it is possible to do what is called a lien strip on a primary residence if the home is worth less than the balance of the first mortgage and the debtor files a Chapter 13 along with a lien strip motion. Of course, she will have to make some payments under Chapter 13 for a period of either 3-5 years and successfully complete the Plan in order to benefit from the lien strip. I assume when you say wife took out a line of credit, that you did not sign the promissory note on that loan. If she chooses to file Chapter 7, while her legal obligation to repay on the promissory note will be discharged, the creditor can collect the collateral through a foreclosure either while the case is pending after doing a motion for relief of stay OR after the chapter 7 case closes. But what will actually happen is not so cut and dry because I said the creditor CAN foreclose, it's only a guess whether an equity line of credit will proceed with foreclosure particularly if the home's value is below the balance of the first mortgage as the equity line creditor would go through an expense of foreclosure but gain nothing from foreclosure sale profits as the first mortgage must be paid first). There are other options that she could explore but whether she will is a matter of choice and also qualifications: a loan modification or a settlement where she offers a sum in exchange for releasing her liability. I can't speculate on the outcome.