Antibiotics are generally thought of as a cure-all for any infection. However, because they work based on biochemistry, their mechanism of action dictates what infections they work on!
Antibiotics against bacteria target specific structures or proteins that the bacteria produce. Many, like the penicillins or other beta-lactams, go after the cell wall. Others, like fluoroquinilones or macrolides, attack the bacterial ribosome, which is markedly different from the human ribosome. Of course, being a virus, Hepatitis B cannot be attacked by trying to go after bacterial structures!
Ideally, Hepatitis B is prevented through vaccination, where viral fragments are injected to generate an immune response that can mature into a long-term defense. However, many people who do not have this protection do get infected, and if their immune system cannot handle the virus on its own, they need treatment.
Clearly, the solution is to go after viral structures! The amount of viral-specific material is scant compared to bacteria, but we do have drugs to combat a HBV (Hepatitis B Virus) infection. Generally, they center on tricking the virus into trying to put a chemical into its DNA that prevents it from continuing replication. Humans and bacteria are not affected by these chemicals because only the HBV--and some other virus'--proteins can prime the drug so that it can fit on the DNA chain.
The take away message here is that each type of organism has different biochemical aspects to it. To combat any given infection, you need to attack the specific structures in the specific infection, or you do nothing. In fact, you can do worse than nothing considering the many side effects these medications can have!
Hepatitis B is caused when the body gets infected by a virus called Hepatitis B Virus or HBV. According to the Macmillan dictionary, an antibiotic is a drug that cures illnesses and infections caused by bacteria.
A majority of people think antibiotics as drugs that treat microbial infections. Though, nowadays, there are antibiotics that cure fungal and protozoan infections also, they have, in the strict terms, no role to play when it comes to viral infections.
This happens because an antibiotic works by conquering the bacterial cellular reproduction and blocking synthesis of new cell wall. But viruses, as we know, possess completely different machinery (They are nothing but DNA/RNA coated by proteins, surrounded by a lipid membrane). They lack an independent cell structure like bacteria. Hence the antibiotics that target bacteria are unable to kill viruses. This is the reason why taking an antibiotic does not help during Hepatitis B and, for that matter, other viral infections like common cold, Polio, Tetanus, Rabies .
Viral infections need a completely different approach. The virus multiplies several copies of its genome in the host and this is how an infection spreads. A popular technique against viral infections is pre-infection immunization via vaccination (Hepatitis B also has a preventive vaccination).
In this, dead virus particles or fragments are injected into the body so that the body develops immunity and produces antibodies against the virus (This technique, in fact, pays tributes to Edward Jenner who first developed a vaccine for the fatal viral disease, Chicken pox).