Short answer. Not under the Labor Code any more. The article that expressly counted family drivers as household service was repealed by Republic Act No. 10361, the Batas Kasambahay. Whether a particular family driver is a kasambahay is now answered by that Act's own definition, not by the old Code.
What the law says
This Chapter shall apply to all persons rendering services in households for compensation.
Labor Code, Article 141 — Coverage Of Household Service. Read the full provision →
What the law says
including services of family drivers
Labor Code, Article 141 — Coverage Of Household Service. Read the full provision →
What the old article said, and why it no longer decides this
Article 141 of the Labor Code is still printed, and it did put family drivers inside household service in so many words: This Chapter shall apply to all persons rendering services in households for compensation. The definition it gave ran to services in the employer's home and ended with the phrase including services of family drivers. That article was expressly repealed by Republic Act No. 10361 (2013), the Batas Kasambahay, whose repealing clause struck out the entire Labor Code chapter on the employment of househelpers. A repealed definition cannot settle a live question. Anyone answering this from the Code text alone is answering from a provision that is no longer in force.
Where the question is decided now
Republic Act No. 10361 supplies its own definition of who is a kasambahay and its own list of who falls outside it. That definition, and the rules issued under the Act, are what a family driver's status turns on today, and the Act does not simply reproduce the old Labor Code wording. Do not assume the old inclusion carried over automatically. If the status of a family driver matters to you, read the definition section of the Act itself rather than the repealed Code, because that is where any argument either way will start and where a labour officer or a court will look first.
Why the label matters so much
The classification is not a technicality. It decides which minimum wage applies, whether a written contract and registration are required, what benefits are owed, how the employment may lawfully be ended and where a complaint is brought. A driver who is a kasambahay under the Act draws the protections that Act gives. A driver who falls outside it is an ordinary employee or is governed by the general law on services, with a different set of rules. The answer changes real money and real remedies, which is exactly why it should not be taken from a repealed article.
What to do if you are the driver, or the household
Write down what the work actually is: who directs it, whether the driving is purely for the family or partly for a business, where the person sleeps, how and how often the pay is given, and whether there is a written contract. Status under the law follows the real arrangement rather than the job title used at home. Then measure that arrangement against the definition in Republic Act No. 10361. This page is general legal information about which law now governs the question, not advice on any particular household, and no page can promise how a given set of facts will be classified.