The petitioning company files and ordinarily bears the petition costs. Whatever the arrangement, put it in writing before filing and check the amounts against the current USCIS fee schedule rather than an estimate.
Write the cost split down before anyone files
The employer is the petitioner in an L-1B case, so the company signs the petition and deals with USCIS. Petition fees, any premium processing fee and counsel's fees are ordinary business expenses and are usually the company's, while personal costs such as passport renewals, travel and the family's medical or relocation expenses are usually the household's. Disputes arise when nobody wrote it down and a request for evidence adds unbudgeted legal work months later. Agree the split in the assignment letter, including who pays if the petition is refused and who pays for an extension. Take the fee figures from the current USCIS fee schedule at the time of filing, because published amounts change and a budget built on last year's numbers is wrong in a way nobody notices until the cheque is written.
Hypothetical example: a medical-device supplier expects the transferee to pay counsel and recover the money through a discretionary bonus. The first review should identify the required petition fees, premium-processing choice, relocation costs and any response-to-evidence reserve in a written assignment letter. The signed assignment letter and current fee schedule settle who bears each item. Decide that allocation before filing, because a reimbursement dispute can delay the evidence work even when the employee's specialized knowledge is well documented.