Question: "Is a home church a true Biblical church?"
Answer: Churches in the New Testament era were indeed small assemblies that met in homes (Acts 2:46; 20:20). So the practice is certainly biblically allowable. There also seem to be some good reasons to have house churches as opposed to large gatherings: greater intimacy, stronger relationships, more comfortable worship, single-mindedness, etc. The fact that large churches usually have their own small groups that meet in homes speaks to this fact. Several considerations should be made, however, concerning the reasons for creating and/or attending a house church.
First, the fact that first-century Christians did something does not establish it as a pattern for all generations to follow (unless there is also a clear command to do so elsewhere). Simply because Scripture records an event or practice does not, of itself, establish a command (nor, in some cases, even approval!). So, for example, the fact that early Christians often sold all they owned and shared the profits (Acts 2:44-45) among other believers does not mean that we must do so today (although it certainly would be acceptable). So we should not think that home churches are any more "biblical" in this sense.
Second, there was a perfectly practical reason for the early church to meet in homes. Where else would they meet? There were no church buildings, YMCA's, grammar schools, or movie theaters that could hold large groups. Further, even if there was room somewhere, during this time of persecution by the Romans, a public gathering of hundreds or thousands of people would simply not be safe. Thus, it might not have been by design that the early church met in small groups. It is even possible that they would have preferred large meetings (as Jews would have been accustomed to), but they simply could not manage it. So we should also not think that home churches are any more "spiritual" than large churches.
Third, home churches that are started in an effort to counter "the institutional church" could be questionable. While often listing the above reasons to more closely align with the biblical model, the real reason often seems to be displeasure with large church movements. While these complaints are often valid, it can lead to an egalitarian, "us vs. them" mentality that should be avoided.
In addition to the above considerations regarding motive, one final caution concerns the issue of accountability. For Protestant churches, the Bible alone is the guide in matters of faith and practice. However, few people have the time to gain the skills and knowledge to accurately handle the word of God (2 Timothy 3:14-16). In classical education theology was taught last—for it builds on many other disciplines that cannot be learned from the Bible alone. Therefore, some degree of higher education was usually sought before one became a teacher of the word (James 3:1). The popular view today, however, is that the Holy Spirit teaches believers directly through the Bible. This idea might lead people to believe that whatever the group teaches is from God and is therefore safe from error. But the Bible does not teach that this is the case, and it is clear that most believers disagree on at least some issues, and most simply end up "interpreting" the Bible according to their churches' teaching anyway.
The answer to the interpretation issue requires another article, but the problem it creates becomes more ominous when dealing with home churches. The New Testament is full of warnings against heresies coming from within the church. Since it was written in the first century, these would actually be warnings regarding house churches. While this problem is certainly not limited to house churches, there is clearly no guarantee of protection from false teaching simply because the church changes its meeting format. Further, because home churches function as independent small groups, they need have no accountability to anyone but themselves. This makes it much more difficult to judge their teachings (in fact, the Jehovah's Witnesses cult began in exactly this manner). In contrast, larger congregations benefit from a plurality of elders, spiritually mature men (Titus 1:5-9) who are overseers of the flock, protecting them from false doctrine.
In conclusion, there is nothing unbiblical about Christians gathering together regularly in houses, or large buildings, or any other appropriate venue. The Bible does not, in fact, give any guidelines as to the proper gathering size or location. What it does do is explain what is to take place at those meetings (Acts 2:42; 1 Corinthians 16:2; 1 Timothy 4:13; 2 Timothy 4:2). So long as biblical teachings (orthodoxy) and practices (orthopraxy) are undertaken by those in assembly, it really does not matter what meeting format one chooses.